Difference between revisions of "2022 AMC 10A Problems/Problem 6"
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<cmath>\begin{align*} | <cmath>\begin{align*} | ||
\left|a-2-\sqrt{(a-1)^2}\right| &= \left|a-2-|a-1|\right| \\ | \left|a-2-\sqrt{(a-1)^2}\right| &= \left|a-2-|a-1|\right| \\ | ||
− | &=\left|a-2-(-a | + | &=\left|a-2-(1-a)\right| \\ |
&=\left|2a-3\right| \\ | &=\left|2a-3\right| \\ | ||
&=\boxed{\textbf{(A) } 3-2a}. | &=\boxed{\textbf{(A) } 3-2a}. |
Revision as of 18:13, 16 November 2022
Problem
Which expression is equal to for
Solution 1
We have
~MRENTHUSIASM
Solution 2
Assume that Then, the given expression simplifies to
:
Then, we test each of the answer choices to see which one is equal to
:
The only answer choice equal to for
is
-MathWizard09
Video Solution 1 (Quick and Easy)
~Education, the Study of Everything
See Also
2022 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.